Circuit With Everything (old exam problem) A circuit is assembled as above and t

Question

Circuit With Everything (old exam problem) A circuit is assembled as above and then some time is allowed to pass so that the whole circuit comes to a steady state. All questions below refer to the circuit in the steady state: Approximately how much time is required to ensure that the circuit will be in a steady state? Explain your answer. In the steady state, what is the voltage drop across the inductor? Explain your answer. In the steady state, what is the current through the battery labeled "B"? Explain your answer. (Harder) In the steady state, what is the voltage drop across the capacitor?

Explanation / Answer

in steady state, capacitor is open circuit and inductor is short circuit.

part a:

5-6 time constants is required to ensure the circuit is in steady state.

part b:
in steady state, inductor behaves as a short circuit.

so voltage drop across the inductor is zero volts.

part c:

the equivalent circuit becomes:

5 ohms and 5 ohms are in series.

net reistance is 10 ohms

this is in parallel with 10 ohms.

(15 ohms resistance is open circuited and hence wont figure in equivalent circuit)

net resistance of 10 ohms in parallel with 10 ohms=10*10/(10+10)=5 ohms

5 ohms is in series with 10 ohms

so equivalent resistance=10+5=15 ohms

so current=(1.5+1.5)/15=0.2 A

part d:

voltage drop across capacitor=voltage drop across the 10 ohms resistance which is in series with inductor

=1.5+1.5-voltage drop across the 10 ohms resistance which is in series

=3-10*current

=3-10*0.2=1 volts

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